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Calculate the inverse secant (arcsec) of a value. Find the angle whose secant equals the input.
| x | arcsec(x) in Degrees | arcsec(x) in Radians |
|---|---|---|
| -2 | 120° | 2π/3 |
| -1.414 | 135° | 3π/4 |
| -1.155 | 150° | 5π/6 |
| -1 | 180° | π |
| 1 | 0° | 0 |
| 1.155 | 30° | π/6 |
| 1.414 | 45° | π/4 |
| 2 | 60° | π/3 |
arcsec(x) = arccos(1/x)
d/dx[arcsec(x)] = 1/(|x|√(x²-1))
arcsec(-x) = π - arcsec(x)
arcsec(x) = arccos(1/x)
Because sec(θ) = 1/cos(θ), and since |cos(θ)| ≤ 1, we have |sec(θ)| ≥ 1. So there's no angle whose secant is between -1 and 1.
Use arcsec(x) = arccos(1/x). Just take 1/x and use the arccos function.
Because sec(π/2) is undefined (cos(π/2) = 0, so 1/cos(π/2) is undefined). The angle 90° has no secant value.